x^4+x^2*127000-205700000000=0

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Solution for x^4+x^2*127000-205700000000=0 equation:


Simplifying
x4 + x2 * 127000 + -205700000000 = 0

Reorder the terms for easier multiplication:
x4 + 127000x2 + -205700000000 = 0

Reorder the terms:
-205700000000 + 127000x2 + x4 = 0

Solving
-205700000000 + 127000x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '205700000000' to each side of the equation.
-205700000000 + 127000x2 + 205700000000 + x4 = 0 + 205700000000

Reorder the terms:
-205700000000 + 205700000000 + 127000x2 + x4 = 0 + 205700000000

Combine like terms: -205700000000 + 205700000000 = 0
0 + 127000x2 + x4 = 0 + 205700000000
127000x2 + x4 = 0 + 205700000000

Combine like terms: 0 + 205700000000 = 205700000000
127000x2 + x4 = 205700000000

The x term is 127000x2.  Take half its coefficient (63500).
Square it (4032250000) and add it to both sides.

Add '4032250000' to each side of the equation.
127000x2 + 4032250000 + x4 = 205700000000 + 4032250000

Reorder the terms:
4032250000 + 127000x2 + x4 = 205700000000 + 4032250000

Combine like terms: 205700000000 + 4032250000 = 209732250000
4032250000 + 127000x2 + x4 = 209732250000

Factor a perfect square on the left side:
(x2 + 63500)(x2 + 63500) = 209732250000

Calculate the square root of the right side: 457965.337116249

Break this problem into two subproblems by setting 
(x2 + 63500) equal to 457965.337116249 and -457965.337116249.

Subproblem 1

x2 + 63500 = 457965.337116249 Simplifying x2 + 63500 = 457965.337116249 Reorder the terms: 63500 + x2 = 457965.337116249 Solving 63500 + x2 = 457965.337116249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-63500' to each side of the equation. 63500 + -63500 + x2 = 457965.337116249 + -63500 Combine like terms: 63500 + -63500 = 0 0 + x2 = 457965.337116249 + -63500 x2 = 457965.337116249 + -63500 Combine like terms: 457965.337116249 + -63500 = 394465.337116249 x2 = 394465.337116249 Simplifying x2 = 394465.337116249 Take the square root of each side: x = {-628.064755512, 628.064755512}

Subproblem 2

x2 + 63500 = -457965.337116249 Simplifying x2 + 63500 = -457965.337116249 Reorder the terms: 63500 + x2 = -457965.337116249 Solving 63500 + x2 = -457965.337116249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-63500' to each side of the equation. 63500 + -63500 + x2 = -457965.337116249 + -63500 Combine like terms: 63500 + -63500 = 0 0 + x2 = -457965.337116249 + -63500 x2 = -457965.337116249 + -63500 Combine like terms: -457965.337116249 + -63500 = -521465.337116249 x2 = -521465.337116249 Simplifying x2 = -521465.337116249 Reorder the terms: 521465.337116249 + x2 = -521465.337116249 + 521465.337116249 Combine like terms: -521465.337116249 + 521465.337116249 = 0.000000000 521465.337116249 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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